Snowballs make cool science

The chilling reminder of looking outdoors is that snow may finally be sticking around this season.

But apart from the physical stress of scraping windshields and shoveling sidewalks, wintery weather bestows stimulating opportunities for scientific study. How so? Let’s turn the scholarly lens on snowballs.

“Making a snowball is sort of like making a diamond: It requires some pressure and some heat because you’ve got to squeeze that snow together,” explained Brad E. Peroney Jr., program development coordinator at the Carnegie Science Center. “When carbon is put under tremendous pressure and temperature it can be crystallized into a diamond, so by putting some pressure and temperature, although much lower, we can turn our snow into snowballs and we can give them that nice snowball shape.”

But even though it is the season — while temperatures will remain above freezing for most of the time, forecasts call for snow at least one day each week on into February — not all snow is good snowball snow, cautioned Peroney. The best type tends to arrive “earlier in the winter, around December, before it gets really cold like in February and March.”

The reason is crystallization speed. Humidity and temperature affects the process whereby water freezes and crystallizes to form snow, he explained. Warmer days with greater humidity cause ice crystals to grow slower. Alternatively, colder days enable the ice crystals to “grow really fast” and not as big, resulting in the kind of “powdery and hard to pack down” snow.

So an ideal climate is “right around freezing or the upper 20 degree range when you can still feel some of that humidity. In my experience that’s when I see the best snowball snow falling.”

But even in a perfect seasonal setting there is still so much to consider, such as identifying the optimal snowball size and best method for stacking, said several scholarly snow enthusiasts.

“As far as size goes there can be a lot of temptation to make the biggest snowball that you can possibly throw, but everyone is going to find that the best size for them is just about the size of their own fist,” said Peroney.

“Maybe it’s a perfect ball whose diameter is 6 inches,” suggested Menachem Lazar, a Squirrel Hill native and applied mathematician at the University of Pennsylvania in Philadelphia.

As for storing your cache of snowballs, the 17th century’s Johannes Kepler, a mathematician and astronomer, conjectured that equally sized spheres are most densely packed in arrangements of cubic close packing and hexagonal close packing. A classic example of such stacking occurs in the case of oranges in a crate. Once the floor of the crate is covered with oranges, new layers are added above in an almost pyramid-like manner.

Though Kepler suggested the stacking tactic as the best strategy, nearly 400 years passed until a proof was offered. In a process spanning from 1998 until 2014, Thomas Hales, who is now Mellon Professor at the University of Pittsburgh, employed sophisticated mathematical techniques and massive computer calculations to confirm Kepler’s belief.

So in the case of snowballs, which are all roughly the same size, “you want to keep them close together,” said Lazar. Partially because of Kepler’s conjecture and also because “you don’t need to walk far every time you want to pick up your next shot.”

But even before throwing a snowball there is still something to assess, said Elli Kanal, like “from a bio-standpoint, how quickly your hands will freeze if you play with snow without gloves.”

Kanal is a data scientist and technical manager at Carnegie Mellon University’s Software Engineering Institute, and the author of “Shady Acres,” a blog on science, programming and writing.

When it comes to a good snowball fight, “it’s tempting to stay out all day, but it’s good to take a break and go inside,” said Peroney.

The concern is frostbite, offered Kanal. “Holding snowballs with the bare hands for a few seconds probably won’t cause any problems, but playing through an entire snowball fight without gloves will probably result in at least mild frostbite, if not worse.”

Playing outdoors this time of year is “obviously a lot of fun but we also want to make sure that we are being safe,” agreed Peroney. So apart from retrieving snow from grassy areas without gravel, “make sure you don’t pick up foreign objects that can hurt somebody, make sure that your snow is the right color and make sure it is not soiled by biological processes.”

With science and safety in mind, snowballs take on a whole new shape. So during this wintery season, whether you are trying to figure out how many to stack or the number that can fit in the back of your snowmobile, said Lazar, remember “sometimes very casual normal everyday problems can motivate beautiful mathematics.”

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